Diffusion approximations of the geometric Markov ...
|Title||Diffusion approximations of the geometric Markov renewal processes and option price formulas|
|Author(s)||S. Anatoliy, Shafiqul Islam|
|Journal||International Journal of Stochastic Analysis|
|Abstract||We consider the geometric Markov renewal processes as a model for a security
market and study this processes in a diffusion approximation scheme. Weak convergence
analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion
scheme are presented. We present European call option pricing formulas in the case of
ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.
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